The principal aim is to investigate the clinical and cost-effectiveness of adding lamotrigine to usual care for adults with Borderline Personality Disorder. To achieve this, we will: - Test whether adding lamotrigine to usual care for adults with Borderline Personality Disorder improves mental health over a 52 week period, in comparison to a placebo control. - Examine whether the addition of lamotrigine to usual care for adults with Borderline Personality Disorder improves social functioning and quality of life, reduces the incidence of suicidal behaviour, and lowers the amount of antipsychotic and other psychotropic medication that people are prescribed, in comparison to a placebo control. - Compare the incidence of side effects among those prescribed lamotrigine in addition to usual care for adults with Borderline Personality Disorder, in comparison to a placebo control. - Examine the cost, cost-utility and cost-effectiveness of adding lamotrigine to usual care for a